David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Technical results about the time dependence of eigenvectors of reduced density operators are considered, and the relevance of these results is discussed for modal interpretations of quantum mechanics which take the corresponding eigenprojections to represent deﬁnite properties. Continuous eigenvectors can be found if degeneracies are avoided. We show that, in ﬁnite dimensions, the space of degenerate operators has co-dimension 3 in the space of all reduced operators, suggesting that continuous eigenvectors almost surely exist. In any dimension, even when degeneracies are hit, we ﬁnd conditions under which a theorem due to Rellich can provide continuous eigenvectors. We use this result to formulate an extended version of the modal interpretation. We also discuss eigenvector instability which we argue poses a serious problem for the modal interpretation, even in our extended version. Many examples are given to illustrate the mathematics.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
Dennis Dieks (2007). Probability in Modal Interpretations of Quantum Mechanics. Studies in History and Philosophy of Science Part B 38 (2):292-310.
Similar books and articles
George Goguadze, Carla Piazza & Yde Venema (2003). Simulating Polyadic Modal Logics by Monadic Ones. Journal of Symbolic Logic 68 (2):419-462.
Gary M. Hardegree (1980). Micro-States in the Interpretation of Quantum Theory. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:43 - 54.
Graciela Domenech, Hector Freytes & Christian de Ronde, The Contextual Character of Modal Interpretations of Quantum Mechanics.
Joseph Berkovitz & Meir Hemmo (2005). Modal Interpretations of Quantum Mechanics and Relativity: A Reconsideration. [REVIEW] Foundations of Physics 35 (3):373-397.
Olimpia Lombardi, Sebastian Fortin, Mario Castagnino & Juan Sebastián Ardenghi (2011). Compatibility Between Environment-Induced Decoherence and the Modal-Hamiltonian Interpretation of Quantum Mechanics. Philosophy of Science 78 (5):1024-1036.
Olimpia Lombardi & Mario Castagnino (2008). A Modal-Hamiltonian Interpretation of Quantum Mechanics. Studies in History and Philosophy of Science Part B 39 (2):380-443.
Michael Dickson (1994). Wavefunction Tails in the Modal Interpretation. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:366 - 376.
Pieter E. Vermaas (1999). A Philosopher's Understanding of Quantum Mechanics: Possibilities and Impossibilities of a Modal Interpretation. Cambridge University Press.
Laura Ruetsche (2003). Modal Semantics, Modal Dynamics and the Problem of State Preparation. International Studies in the Philosophy of Science 17 (1):25 – 41.
Added to index2009-01-28
Total downloads6 ( #237,968 of 1,692,205 )
Recent downloads (6 months)4 ( #59,665 of 1,692,205 )
How can I increase my downloads?